We endow the set of probability measures on a weighted graph with a Monge–Kantorovich metric induced by a function defined on the set of edges. The graph is assumed to have n vertices and so the boundary of the probability simplex is an affine (n − 2)-chain. Characterizing the geodesics of minimal length which may intersect the boundary is a challenge we overcome even when the endpoints of the geodesics do not share the same connected components. It is our hope that this work will be a preamble to the theory of mean field games on graphs.
Accepté le :
DOI : 10.1051/cocv/2018052
Mots-clés : Optimal transport on simplexes, manifold with boundary, Geodesic, Hamilton–Jacobi equations on graphs
@article{COCV_2019__25__A78_0,
author = {Gangbo, Wilfrid and Li, Wuchen and Mou, Chenchen},
title = {Geodesics of minimal length in the set of probability measures on graphs},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018052},
mrnumber = {4039140},
zbl = {07194617},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2018052/}
}
TY - JOUR AU - Gangbo, Wilfrid AU - Li, Wuchen AU - Mou, Chenchen TI - Geodesics of minimal length in the set of probability measures on graphs JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2018052/ DO - 10.1051/cocv/2018052 LA - en ID - COCV_2019__25__A78_0 ER -
%0 Journal Article %A Gangbo, Wilfrid %A Li, Wuchen %A Mou, Chenchen %T Geodesics of minimal length in the set of probability measures on graphs %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2018052/ %R 10.1051/cocv/2018052 %G en %F COCV_2019__25__A78_0
Gangbo, Wilfrid; Li, Wuchen; Mou, Chenchen. Geodesics of minimal length in the set of probability measures on graphs. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 78. doi : 10.1051/cocv/2018052. http://www.numdam.org/articles/10.1051/cocv/2018052/
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